Given your set-up for A, ajj, C1, C2, C3, k and d compute the following. Show your work so an interested peer can follow along. art 1: Vectors a. Find C1 + 413 . C2. b. Find C1 . C2. c. Find the angle between C1 and C2. d. Describe the plane orthogonal to the vector C3. art 2: Matrices a. Find the determinant of A. b. Find the trace of A c. Find B = A . AT . Is B symmetric? d. Find the inverse of A. art 3: Basic combinatorics n ice cream shop has k different flavors of ice cream. How many different ways are there to select d scoops of ice cream in each of the following scenarios? k and d are the numbers you calculated above. Make sure your exposition demonstrates an understanding of the argument and formulas used, not ist applying the formula to each instance. a. No flavor can be repeated and the order in which the scoops are chosen matter. E.g., you cannot have three scoops, including vanilla, vanilla, and strawberry. Also, having chocolate at the bottom and strawberry on top is different from having strawberry at the bottom and chocolate on top. b. No flavor can be repeated and the order in which the scoops are chosen does not matter. E.g., you cannot have three scoops, including vanilla, vanilla, and strawberry. Also, having chocolate at the bottom and strawberry on top is the same as having strawberry at the bottom and chocolate on top. c. Flavors can be repeated and the order in which the scoops are chosen matters. E.g., you can have three scoops, including vanilla, vanilla, and strawberry. Also, having chocolate at the bottom and strawberry on top is different from having strawberry at the bottom and chocolate on top. d. Flavors can be repeated and the order in which the scoops are chosen does not matter. E.g., you can have three scoops, including vanilla, vanilla, and strawberry. Also, having chocolate at the bottom and strawberry on top is the same as having strawberry at the bottom and chocolate on top. art 4: Systems of linear equations. a. Write out explicitly the system of equations implied by the matrix equation: A b. Provide an economic interpretation of this system of equations. Within that interpretation, what do we learn by solving the system? c. Use the method of Gaussian Elimination to solve the system of equations from a. (Show your work) d. Does the system of equations have exactly one solution? Infinitely many? or none? Why? e. If there are infinitely many solutions: Adjust the coefficients as little as possible, so that there is a unique solution. Otherwise: Adjust the coefficients as little as possible, so that there are infinitely many solutions f. If there is no solution: Adjust the coefficients as little as possible, so that there is a unique solution. Otherwise: Adjust the coefficients as little as possible, so that there is no solution